(b) Estimate the minimum potential difference needed to reduce `AI_(2)O_(3)` at `500^(@)C` The gibbs energy change for the decomposition reaction `2/3AI_(2)O_(3)rarr4/3AI+O_(2)`is 960 kJ (F=96500 C `mol^(-1))`

Explanation

`Al_2 O_3 (Al^(3+) + 3O^(2-)) to 2 Al + (3)/(2) O_(2)`
This reaction involves 6 electrons , n = 6
`therefore (2)/(3) Al_(2) O_(3) to (4)/(3) Al + O_(2) , n = (6 xx 2)/(3) = 4e^(-)`
`Delta G = - nFE`
`Delta G = 960 xx 10^(3) J , n = 4 , F = 96500 C mol^(-1)`
`therefore 960 xx 10^(3) = - 4 xx 96500 xx E `
or `E = - (960 xx 10^(8))/(4 xx 96500) = -2.487` V
`therefore` Minimum potential difference needed to reduce `Al_2 O_3 = 2.487 V`.